EduNinja

[Maximum number: 7]

(a)

NOT TO SCALE

The diagram shows a field, ABCD with B north of A.
BD is a path across the field.
$A B=85 \mathrm{~m}, A D=72 \mathrm{~m}, B D=129 \mathrm{~m}$ , angle $B D C=39^{\circ}$ and angle $B C D=60^{\circ}$ .

[ 7 ]

(i)

Show that angle $A B D=31.6^{\circ}$ , correct to 1 decimal place.

[ 4 ]

$[\cos=]\frac{85^2+129^2-72^2}{2\times85\times129}$
M1 for $72^2=85^2+129^2-2\times85\times129\cos ABD$ $31.58\ldots$
A1 for 0.851 to 0.852 or $\frac{9341}{10965}$ or equivalent fraction

(ii)

Find the shortest distance from A to BD.

[ 3 ]

44.5 or 44.51 to 44.54
M2 for implicit correct method, e.g. $\frac{d}{85}=\sin31.6^\circ$ oe
or M1 for recognition that the line from A is perpendicular to BD

[Maximum number: 5]

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
$A C=15 \mathrm{~m}, B C=8 \mathrm{~m}$ and $A B=20 \mathrm{~m}$ .
BP and CQ are vertical poles of different heights.
$B P=3 \mathrm{~m}$ and $C Q=4 \mathrm{~m}$ .
AQ and PQ are straight wires.

(a)

Calculate the length of AQ.

[ 2 ]

15.5 or 15.52 to 15.53
M1 for $15^2+4^2$ oe

(b)

Calculate the angle of elevation of Q from P.

[ 3 ]

7.1 or 7.13 or 7.125 to 7.126
M2 for $\tan P=\frac{4-3}{8}$ oe or M1 for vertical line =4-3

All question bank results loaded

CAIE IGCSE Mathematics Extended E6.2 Right Angled Triangles Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)